Functional central limit theorems for persistent Betti numbers on cylindrical networks

• Verfasst von: Krebs, Johannes [VerfasserIn]
• Verfasst von: Hirsch, Christian [VerfasserIn]
• Titel: Functional central limit theorems for persistent Betti numbers on cylindrical networks
• Verf.angabe: Johannes Krebs, Christian Hirsch
• Jahr: 2022
• Umfang: 20 S.
• Fussnoten: First published: 12 March 2021 ; Gesehen am 17.04.2023
• Titel Quelle: Enthalten in: Scandinavian journal of statistics
• Ort Quelle: Oxford : Wiley-Blackwell, 1974
• Jahr Quelle: 2022
• Band/Heft Quelle: 49(2022), 1, Seite 427-454
• ISSN Quelle: 1467-9469
• DOI: doi:10.1111/sjos.12524
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: functional central limit theorems
• Sach-SW: goodness-of-fit tests
• Sach-SW: graphical networks
• Sach-SW: persistent Betti numbers
• Sach-SW: stochastic geometry
• Sach-SW: topological data analysis
• K10plus-PPN: 1842789538
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Čech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.